Eta-quotients and theta functions

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• 作者：Robert J. Lemke Oliver ^{rlemkeo@emory.edu lemkeoliver@gmail.com}
• 关键词：Modular forms ; qq-series ; Eta-quotients ; Theta functions
• 刊名：Advances in Mathematics
• 出版年：2013
• 出版时间：10 July, 2013
• 年：2013
• 卷：241
• 期：Complete
• 页码：1-17
• 全文大小：215 K

文摘

The Jacobi Triple Product Identity gives a closed form for many infinite product generating functions that arise naturally in combinatorics and number theory. Of particular interest is its application to Dedekind¡¯s eta-function , defined via an infinite product, giving it as a certain kind of infinite sum known as a theta function. Using the theory of modular forms, we classify all eta-quotients that are theta functions.